Neuro genetic key based recursive modulo 2 substitution using mutated character for online wireless communication (ngkrmsmc)

International Journal of Computational Science and Information Technology (IJCSITY) Vol.1, No.4, November 2013

DOI : 10.5121/ijcsity.2014.1404 49

NEURO GENETIC KEY BASED RECURSIVE

MODULO-2 SUBSTITUTION USING MUTATED

CHARACTER FOR ONLINE WIRELESS

COMMUNICATION (NGKRMSMC)

Arindam Sarkar and J. K. Mandal

Department of Computer Science & Engineering, University of Kalyani, W.B, India

ABSTRACT In this paper, a neural genetic key based technique for encryption (NGKRMSMC) has been proposed

through recursive modulo-2 substitution using mutated character code generation for online wireless

communication of data/information. Both sender and receiver get synchronized based on their final output.

The length of the key depends on the number of input and output neurons. Coordinated matching weight

vectors assist to generate chromosomes pool. Genetic secret key is obtained using fitness function, which is

the hamming distance between two chromosomes. Crossover and mutation are used to add elitism of

chromosomes. At first mutated character code table based encryption strategy get perform on plain text. .

Then the intermediate cipher text is yet again encrypted through recursive positional modulo-2 substitution

technique to from next level encrypted text. This 2nd level intermediate cipher text is again encrypted to

form the final cipher text through chaining and cascaded xoring of neuro genetic key with the identical

length intermediate cipher text block. Receiver will perform same symmetric operation to get back the plain

text using identical key.

KEYWORDS Neuro Genetic Key based base Recursive Modulo-2 Substitution using Mutated Character (NGKRMSMC),

weight vector, input vector, chaining, neuro genetic key.

1. INTRODUCTION

In cryptography there are wide variety of techniques are available with some pros and cons to

protect data [1]-[3], [7]. These algorithms have their merits and shortcomings. For Example in

DES, AES algorithms [9] the cipher block length is nonflexible. ANNRPMS [1] and ANNRBLC

[2] allow only one cipher block encoding. In this paper a neural training based genetic algorithm

guided online encryption technique for wireless communicationhas been proposed.

The organization of this paper is as follows. Section 2 of the paper deals with the proposed neuro

synchronization and genetic key generation technique and also random block length based

cryptographic techniques using mutated character code generation. Session key based technique

has been discussed in section 3. Example of recursive modulo-2 technique is given in section 4.

Complexity of the algorithm has been presented in section 5. Results are described in section 6.

Conclusions are presented in section 7 and references at end.


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2. THE NGKRMSMC TECHNIQUE In proposed technique mutated character code table and recursive positional modulo-2

substitution algorithm is used to encrypt the plain text. This intermediate cipher text is again

encrypted to form the final cipher text using chaining of cascaded xoring of the neuro genetic

secret key. Using identical weight vector receiver performs deciphering process to regenerate the

plain text.

2.1 Neural synchronization scheme & secret key generation

At the beginning of the transmission, a neural network based secret key generation is

performed between receiver and sender. The same may be done through the private channel also

or it may be done in some other time, which is absolutely free from encryption. Fig. 1. shows the

tree based generation process using arbitrary number of nodes (neurons). Corresponding

algorithm and genetic key generation is given in two-sub section 1 and.2.

Figure1 A tree parity machine with K=3 and N=4

Neural synchronization algorithm

Input: - Random weights, input vectors for both neural networks

Output: - Session key .

Method: - Each party (A and B) uses its own (same) tree parity machine. Neural network

parameters: K, N, L values will be identical for both parties and synchronization of the

tree parity machines is achieved.

Parameters:

K - The number of hidden neurons.

N - The number of input neurons connected to each hidden neuron, total (K*N) input neurons.

L - The maximum value for weight {-L..+L}

Step 1. Initialize random weight values.

Step 2. Repeat step 3 to 6 until both sender and receiver get synchronized.

Step 3. Produce random input vector X. Inputs are generated by a third party (say the server) or

one of the communicating parties (figure. 2)


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Figure 2 Neural network for machine A and machine B with K=4 & N=2

Step 4. Compute the values of the hidden neurons

N

j

ijiji xw1

sgn

1

0

1

sgn x

if

if

if

.0

,0

,0

x

x

x

(1)

Step 5. Compute the value of the output neuron

K

i

N

j

ijij xw1 1

sgn

(2)

Step 6. Compare the output values of both tree parity machines by exchanging between the

networks. If Output (A) ≠ Output (B) then go to step 3 else if Output (A) = Output (B) then

Update the weights. In this paper we have used hebbian-learning rule for synchronization

(eq. 3).

BA

iiii xwwi (3)

In each step there may be three possibilities:

1. Output (A) ≠ Output (B): None of the parties updates its weights.

2. Output (A) = Output (B) = Output (E): All the three parties update weights.

3. Output (A) = Output (B) ≠ Output (E): Parties A and B update their weights, but the attacker

cannot do that as the synchronization of two parties are faster than learning of an attacker.

Complexity: O(N) computational steps are required to generate a key of length N. The average

synchronization time up to N=1000 asymptotically one expects an increase of O (log N).

3 SESSION KEY GENERATION USING GENETIC ALGORITHM The method considered indistinguishable matched neural weight vector from the first segment in

the form of blocks of bits with dissimilar size like 8/16/32/64/128/256 to generate the dynamic

chromosomes pool. If neural key is exhausted from the formation of pool at some stage, the key

can be circular right shifted by multiple of 8 bits to generate new key stream.

Step 1. Initially, 200 chromosomes are considered as seeds (every chromosomes has number of

bits identical to 8/16/32/64/128/256 bit) from dynamic pool. Parameters of the genetic algorithm

used are: population size = 200, Crossover probability(CP) = 0.6-0.9 and Mutation

probability(MP) =0.001

Step 2. Hamming distance function is used as a fitness function to evaluate the chromosomes to

get the best individuals for forming the key.


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Step 3. Perform one-point crossover, where a crossover point on the chromosome are elected

randomly, and two parent individuals are interchanged at these points.

Step 4. Mutation is performed by bit flipping.

Step 5. Genetic processing is continued until the optimized key (the master key) is obtained.

3.1 Character Code Table Generation

For the plain text “tree” Fig 3 shows corresponding tree representation of probability of

occurrence of each character in the plain text. Character „t‟ and „r‟ occur once and character „e‟

occurs twice. Preorder traversal get used to find out the character code. Character values are

extracted from the decimal representation of character code. Left branch is coded as „0‟ and that

of right branch „1‟. Table 1 tabulated the code and value of a particular character in the plain text.

Mutated tree is generated using mutation. Fig 4, 5 and 6 are the mutated trees. After mutation new

code values as obtained are tabulated in table 2. Tree having n-1 intermediate nodes can generate

2n-1

mutated trees.

Figure3 Character Code Tree Figure4 Mutated at Position 1,2 & 3,4

Figure5 Mutated at Position 3,4 Figure6 Mutated at Position 1,2

1

4

2 2

1

1

0

0

1

e

t r

4

2 2

1

1

1

1

0

0 e

t r

4

2 2

1

1

1

1 0

0

e

t r

4

2 2

1

1

1

1

0

0 e

t r


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Table 1. Code table

Character of plain text Code Value of that

Character

t 10 2

r 11 3

e 0 0

Table 2. Mutated Code Table

Character Code Value Code Value Code Value

t 01 1 11 3 00 0

r 00 0 10 2 01 1

e 1 2 0 0 1 2

4 RECURSIVE MODULO-2 ENCRYPTION TECHNIQUE Now, plain text characters are already converted into the mutated code using the mutated code

table. Then it is divided into blocks. The decimal equivalent of the block of bits under

consideration is one integral value from which the recursive modulo-2 operation starts. The

modulo-2 operation is performed to check whether integral value is even or odd and the position

of that integral value in the series of natural even or odd numbers is evaluated. Process is carried

out Recursively to a finite number of times, which is exactly the length of the source block. After

each modulo-2 operation, 0 or 1 is pushed to the output stream in MSB-to-LSB order; depending

on the fact whether the integral value is even or odd. In this way intermediate encrypted text is

generated.

Figure7 Algorithm for Recursive Modulo-2 encryption technique.

Thus overall complexity of encryption algorithm is O(L).The key is padded with the recursive

modulo-2 encrypted text block to form the 2nd

level intermediate cipher block. Then the neuro

genetic secret key is use to xored with the same length first 2nd

level intermediate cipher text

block to produce the first final cipher block (neuro genetic secret key XOR with same length

cipher text). This newly generated block again xored with the immediate next block and so on.

Set: P = 0.

LOOP:

Evaluate: Temp = Remainder of DL-P / 2.

If Temp = 0

Evaluate: DL-P-1 = DL-P / 2.

Set: tP = 0.

Else If Temp = 1

Evaluate: DL-P-1 = (DL-P + 1) / 2.

Set: tP = 1.

Set: P = P + 1.

If (P > (L – 1))

Exit.

END LOOP


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This chaining of cascaded xoring mechanism is performed until all the blocks get exhausted. If

the last block size of intermediate cipher text is less than the require xoring block size (i.e. neuro

genetic vector size) then this block is kept unchanged.

Recursive Modulo-2 Decryption Technique

During decryption the encrypted message is xored with the neuro genetic key to extract the

intermediate encrypted stream. Then the intermediate encrypted stream is decomposed into a set

of blocks, each consisting of a fixed number of bits using same rule of encryption. Then perform

the recursive modulo-2 decryption operation. Finally, character code value is decrypted using

character code table to get the plain text. Complexity of this decryption algorithm is also O(L).

Figure 8 Algorithm for Recursive Modulo-2 decryption technique.

Example of Recursive Modulo-2 Operation Consider a separate plaintext (P) as: “Local Area Network”.

The Process of Recursive Modulo-2 Encryption

To generate the source stream of bits, we take the reference of Table 3.

Table 3. Character-to-Byte Conversion for the Text “Local Area Network”

Set: P = L – 1 and T = 1.

LOOP:

If tP = 0

Evaluate: T = Tth even number in the series of natural

numbers.

Else If tP = 1

Evaluate: T = Tth odd number in the series of natural

numbers.

Set: P = P – 1.

If P < 0

Exit.

END LOOP

Evaluate: S = s0 s1 s2 s3 s4 … sL-1, which is the binary equivalent of T


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Message stream of bits S is:

S=01001100/01101111/01100011/01100001/01101100/00100000/01000001/01110010/0110010

1/01100001/00100000/01001110/01100101/01110100/01110111/01101111/01110010/01101011.

Decompose S into a set of 5 blocks, each of the first four being of size 32 bits and the last one

being of 16 bits. During this process of decomposition, we scan S along the MSB-to-LSB

direction. Thus we obtain

S1=01001100011011110110001101100001, S2=01101100001000000100000101110010,

S3=01100101011000010010000001001110, S4=01100101011101000111011101101111,

S5=0111001001101011. For the block S1, corresponding to which the decimal value is

(1282368353)10, the process of encryption is shown below:

1282368353 6411841771 320592089

1 160296045

1 80148023

1 40074012

1

200370060 100018503

0 5009252

1 2504626

0 1252313

0 626157

1 313079

1

1565401 78720

0 39135

0 19568

1 9784

0 4892

0 2446

0 1223

0 612

1 306

0

1530 77

1 39

1 20

1 10

0 5

0 3

1 2

1 1

0 1

1. From this we generate the target

block T1 corresponding to S1 as: T1=11111001001110010000100111001101.

Applying the similar process, we generate target blocks T1, T2, T3, T4 and T5 corresponding to

source blocks S1, S2, S3, S4 and S5 respectively.

T2=01110001011111011111101111001001

T3=01001101111110110111100101011001

T4=10001001000100011101000101011001

T5=1110100110110001.

Now, combining target blocks in the same sequence, we get the target stream of bits T as the

following:

T=11111001/00111001/00001001/11001101/01110001/01111101/11111011/11001001/0100110

1/11111011/01111001/01011001/10001001/00010001/11010001/01011001/11101001/10110001.

After padding the key with the above intermediate cipher text and xoring with the neural secret

key, final encrypted cipher text is generated. This stream of bits, in the form of a stream of

characters, is transmitted as the encrypted message.

The Process of Recursive Modulo-2 Decryption

At the destination end, receiver‟s secret neural key is used to xoring the cipher text to get back the

key and intermediate cipher text. Using secret key, the receiver gets the information on different

block lengths. Using that secret key, all the blocks T1, T2, T3, T4 and T5 are formed as follows:

T1=11111001001110010000100111001101

T2=01110001011111011111101111001001

T3=01001101111110110111100101011001

T4=10001001000100011101000101011001

T5=1110100110110001.

Apply the process of decryption to generate source blocks Si for all Ti, 1 ≤ i ≤5. 32-bit stream is

regenerated S1=01001100011011110110001101100001.”

Key Segment

Segment

size in

bits


56

En

cry

pti

on

& d

ecry

pti

on ti

me

Source size

All the source blocks of bits are regenerated and combining those blocks in the same sequence,

the source stream of bits obtained to get the source message or the plaintext.

5 RESULTS Results are presented in terms of encryption decryption time, Chi-Square test, source file size vs.

encryption time along with source file size vs. encrypted file size. The results are also compared

with existing RSA technique.

Table 4. Encryption / decryption time vs. File size

Encryption Time (s) Decryption Time (s)

Source

(bytes)

NGKRMSMC

ANNRPMS Encrypted

(bytes)

NGKRMSMC

ANNRPMS

18432 5. 98 5. 32 18432 5.52 4.85

23044 8.04 7. 37 23040 7.63 6.96

35425 14.59 13. 98 35425 14.08 13. 37

36242 15.17 14. 53 36242 14.70 14. 01

59398 23.02 22. 39 59398 22.51 21. 88

Table 4 shows encryption and decryption time with respect to the source and encrypted size

respectively.

Figure9 Source size vs. encryption time & decryption time

Encryption /decryption time is marginally high because of incorporation of genetic technique and

mutated character coding.

Table 5 shows Chi-Square value for different source stream size on applying various encryption

algorithms. It is seen that the Chi-Square value of NGKRMSMCC is better compared to the

RBCMPCC algorithm and comparable with values of the RSA technique.


57

Table 5. Source size vs. Chi-Square value

Stream

Size

(bytes)

Chi-Square

value

(TDES)

Chi-Square value

Proposed

NGKRMS MCC

Chi-Square

value

(RBCM

CPCC)

Chi-Square

value

(RSA)

1500 1228.5803 2465.0749 2464.0324 5623.14

2500 2948.2285 5643.5271 5642.5835 22638.99

3000 3679.0432 6759.2956 6714.6741 12800.355

3250 4228.2119 6997.6173 6994.6189 15097.77

3500 4242.9165 10572.7263 10570.4671 15284.728

Figure 10 shows graphical representation of table 5.

Figure10 Source size vs. Chi-Square value

6 COMPLEXITY OF THE TECHNIQUE

The complexity of the technique will be O (L), which can be computed using following three

steps.

Step 1: To generate a key of length N needs O (N) Computational steps. The average

synchronization time is independent of the size N of the networks (up to N=1000). The

complexity of synchronization is O (log N).

Step 2: Complexity of the encryption technique is O (L).

Step 2.1: Corresponding to the source block S = s0 s1 s2 s3 s4… sL-1, evaluate the equivalent

decimal integer, DL. It takes O (L) amount of time.

Step 2.2: Step 3 and step 4 executed exactly L number of times for the values of the

variable P ranging from 0 to (L-1) increasing by 1 after each execution of the loop where

the complexity is O (L) as L no. of iterations are needed.

Step 2.3: Apply modulo-2 operation on DL-P to check if DL-P is even or odd, takes constant

amount of time i.e. O(1).

Step 2.4: If DL-P is found to be even, compute DL-P-1 = DL-P / 2, where DL-P-1 is its position in

the series of natural even numbers. Assign tP = 0. If DL-P is found to be odd, compute DL-P-1

= (DL-P + 1) / 2, where DL-P-1 is its position in the series of natural odd numbers. Assign tP=1

which generates the complexity as O (1).

Step 2.5: evaluate: DL, the decimal equivalent, corresponding to the source block S = s0 s1

s2 s3 s4 … sL-1 which takes O (L) amount of time.


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Step 3: Complexity of the decryption technique is O (L).

Step 3.1: Set P=L-1and T=1.So time complexity of assignments is O (1).

Step 3.2: Complexity of loop is O (L) because L iterations are needed.

Step 3.3: If tP = 0,T = Tth even number in the series of natural even numbers. If tP = 1,T =

Tth odd number in the series of natural even numbers. Complexity is O (1) as it takes

constant amount of times.

Step 3.4: Set P=P-1. This step takes constant amount of time i.e. O(1).

Step 3.5: Complexity to convert T into the corresponding stream of bits S = s0 s1 s2 s3

s4…sL-1, which is the source block is O(L) as this step also takes constant amount of time

for merging s0 s1 s2 s3 s4…sL-1 .

So, overall time complexity of the entire technique is O(L).

7 CONCLUSION

The paper presents a novel approach for generation of secret key using neural synchronization.

This proposed technique allows key exchange through public channel. So likelihood of attack of

the technique is much less than the simple RBCMCCC [4]algorithm.

ACKNOWLEDGEMENTS

The author expresses deep sense of gratitude to the DST, Govt. of India, for financial assistance

through INSPIRE Fellowship leading for a PhD work under which this work has been carried out.

REFERENCES

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(ICRTIT 2011) Conf. BY IEEE, 3-5 June 2011, Madras Institute of Technology, Anna University,

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[7] Dong Hu "A new service based computing security model with neural cryptography"IEEE07/2009.J

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Author

Arindam Sarkar

INSPIRE FELLOW (DST, Govt. of India), MCA (VISVA BHARATI, Santiniketan,

University First Class First Rank Holder), M.Tech (CSE, K.U, University First Class First

Rank Holder). Total number of publications 25.

Jyotsna Kumar Mandal

M. Tech.(Computer Science, University of Calcutta), Ph.D.(Engg., Jadavpur University) in

the field of Data Compression and Error Correction Techniques, Professor in Computer

Science and Engineering, University of Kalyani, India. Life Member of Computer Society of

India since 1992 and life member of cryptology Research Society of India. Dean Faculty of

Engineering, Technology & Management, working in the field of Network Security,

Steganography, Remote Sensing & GIS Application, Image Processing. 25 years of teaching

and research experiences. Eight Scholars awarded Ph.D. and 8 are pursuing. Total number

of publications 267.